The ablative absolute is a neat and, I think, elegant Latin subordinate clause. It is distinguishable from the main clause by a subject noun and a participle, usually the perfect, in the ablative case. It has a rough translation meaning 'This having happened', or 'After this had happened...'. The ablative case makes it distinct from the main clause and describes a state of affairs in which the main clause takes place. An example would be: 'Spartaco victo Crassus Pompeiusque consules facti sunt.' (After Spartacus had been defeated, Crassus and Pompey became consuls.) The fact that it has no direct translation into English actually allows you to be reasonably flexible when translating it. For example, Latin often uses an ablative absolute where English would use two verbs linked by 'and'. So, an alternative translation of the above could be, 'Crassus and Pompey defeated Spartacus and became consuls'. As I said, it's quite neat!